Analysis-suitable unstructured T-splines: Multiple extraordinary points per face

Wei, Xiaodong; Li, Xin; Qian, Kuanren; Hughes, Thomas J.R.; Zhang, Yongjie; Casquero, Hugo

doi:10.1016/j.cma.2021.114494

Cited by 35 publications

(9 citation statements)

References 66 publications

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“…It might be necessary to refine the initial mesh in order to guarantee that extraordinary nodes are sufficiently separated. A construction of analysis-suitable unstructured T-splines over more general meshes, which do not satisfy Assumption 3.12, is presented in [27]. However, there the construction of functions around extraordinary nodes differs from the approach presented here.…”

Section: Unstructured T-spline Spacesmentioning

confidence: 99%

Adaptive Refinement for Unstructured T-Splines with Linear Complexity

Maier¹,

Morgenstern²,

Takacs³

2021

Preprint

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We present an adaptive refinement algorithm for T-splines on unstructured 2D meshes. While for structured 2D meshes, one can refine elements alternatingly in horizontal and vertical direction, such an approach cannot be generalized directly to unstructured meshes, where no two unique global mesh directions can be assigned. To resolve this issue, we introduce the concept of direction indices, i.e., integers associated to each edge, which are inspired by theory on higher-dimensional structured T-splines. Together with refinement levels of edges, these indices essentially drive the refinement scheme. We combine these ideas with an edge subdivision routine that allows for Inodes, yielding a very flexible refinement scheme that nicely distributes the T-nodes, preserving global linear independence, analysis-suitability (local linear independence) except in the vicinity of extraordinary nodes, sparsity of the system matrix, and shape regularity of the mesh elements. Further, we show that the refinement procedure has linear complexity in the sense of guaranteed upper bounds on a) the distance between marked and additionally refined elements, and on b) the ratio of the numbers of generated and marked mesh elements.

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Section: Unstructured T-spline Spacesmentioning

confidence: 99%

Adaptive Refinement for Unstructured T-Splines with Linear Complexity

Maier¹,

Morgenstern²,

Takacs³

2021

Preprint

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“…Isogeometric analysis (IGA) 1,2 makes possible the design and analysis of rods [3][4][5][6][7][8] and shells [9][10][11][12][13][14][15][16][17][18] using the same geometric representation in computer-aided-design (CAD) and finite-element-analysis (FEA) programs. This is accomplished by using the same spline-based representations of the geometry in CAD and FEA programs.…”

Section: Introductionmentioning

confidence: 99%

Extending CAS elements to remove shear and membrane locking from quadratic NURBS‐based discretizations of linear plane Timoshenko rods

Golestanian

Casquero

2023

Numerical Meth Engineering

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Continuous‐assumed‐strain (CAS) elements were recently introduced (Casquero and Golestanian. Comput Methods Appl Mech Eng. 2022; 399:115354.) to remove the membrane locking present in quadratic ‐continuous NURBS‐based discretizations of linear plane curved Kirchhoff rods. In this work, we generalize CAS elements to remove shear and membrane locking from quadratic NURBS‐based discretizations of linear plane curved Timoshenko rods. CAS elements are an assumed strain treatment that interpolates the shear and membrane strains at the knots using linear Lagrange polynomials. Consequently, the inter‐element continuity of the shear and membrane strains is maintained. The numerical experiments considered in this work show that CAS elements excise the spurious oscillations in shear and membrane forces caused by shear and membrane locking. Furthermore, when using CAS elements with either full or reduced integration, the convergence of displacements, rotations, and stress resultants is independent of the slenderness ratio up to while the convergence is highly dependent on the slenderness ratio when using NURBS elements. We apply the locking treatment of CAS elements to quadratic ‐continuous NURBS and the resulting element type is named discontinuous‐assumed‐strain (DAS) elements. Comparisons among CAS and DAS elements show that once locking is properly removed, continuity across element boundaries results in higher accuracy than continuity across element boundaries. Lastly, CAS elements result in a simple numerical scheme that does not add any significant computational burden in comparison with the locking‐prone NURBS‐based discretization of the Galerkin method.

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“…However, shaping complex geometries with single entities appears to be demanding, resulting repeatedly in badly conditioned FE models. One avenue to circumvent this restriction has been the introduction of T-Splines [70,71,82], hierarchic splines [83], and other spline technologies within the scope of IGA, which allowed modeling more sophisticated shapes. However, CAD systems do typically rely on an alternative approach in the shape description, the so-called boundary representation (B-Rep) [73].…”

Section: Introductionmentioning

confidence: 99%

Concepts of data collection for the CAD-integrated isogeometric analysis

Teschemacher

Bauer

Aristio

et al. 2022

Engineering with Computers

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This publication presents required steps for the realization of the pre- and post-processing for the isogeometric analysis and the isogeometric B-Rep analysis, with a focus on the collection of required data. It reveals the essential prerequisites for the preparation and the collection of geometrical information, which are merged with physical information for the creation of numerical models. It addresses both the direct computation on existing CAD drawings and the geometrical design during the preparation of the numerical models. The developments are presented through the example of the open source Rhino plugin Cocodrilo, which shall bring IGA to a larger community, including research and industrial facilities.

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Analysis-suitable unstructured T-splines: Multiple extraordinary points per face

Cited by 35 publications

References 66 publications

Adaptive Refinement for Unstructured T-Splines with Linear Complexity

Adaptive Refinement for Unstructured T-Splines with Linear Complexity

Extending CAS elements to remove shear and membrane locking from quadratic NURBS‐based discretizations of linear plane Timoshenko rods

Concepts of data collection for the CAD-integrated isogeometric analysis

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